For the first time David Moyes looked like he had had enough. He did not say it, of course, but his demeanour spoke volumes – after 11 years of managerial alchemy at Everton he had done all he could and needed a gilt-edged club of the real kind.

It is common knowledge that Moyes has been procrastinating over a new contract, with a hankering after pastures new. He had hoped to crown a decade and more of against-the-odds achievement by winning the FA Cup but his players let him down badly with a palsied performance at home to unfancied Wigan Athletic in Saturday's quarter-final, and their 3-0 defeat could well be personally decisive – the final straw.

The cult of the manager is tediously overdone in an era obsessed with celebrity, but it is legitimate to see this sixth-round tie in those terms. Moyes and Wigan's Roberto Martínez have proved their worth and both deserve a chance at clubs possessed with the wherewithal to fulfil their individual potential.

Moyes has continually had Everton punching above their weight on perennially disadvantageous budgets. Martínez made a big impression at Swansea, where he introduced the attractive style of play that has served the Welsh club so well, and at Wigan he has added to his considerable reputation by keeping Premier League football alive in a rugby league town, where attendances suffer by comparison with those of half the clubs in the Championship.

If, as seems likely, both men move on at the end of the season, it would be no surprise if Martínez, who is very much in the "School of Science" tradition, were to succeed Moyes at Goodison where his cohesive football and eye for a bargain are much admired.

Moyes, interestingly, has spoken of a desire to broaden his experience in Germany's Bundesliga. Saturday's outcome was even more of a shock given the declared priorities of the two managers. Moyes was definitely "Up for the Cup" while Martínez continues to stress that the need to avoid relegation from the Premier League is the be-all and end-all. Strangely, then, it was Wigan who played as if Wembley was their ultimate motivation, Everton's laissez-faire attitude suggesting they were the ones preoccupied with the league.

The match was won and lost in a volcanic four-minute eruption around the half-hour when all three goals were scored. Moyes guessed it was not to be Everton's day when, uncharacteristically, they conceded the first through a feeble response to a corner, headed in at the far post by Maynor Figueroa.

Within a minute they were further behind, Phil Neville passing straight to young Callum McManaman, who finished with precocious aplomb.

The best strike of all came in the 33rd minute when Jordi Gómez, from the edge of the D, bent a low shot just inside Jan Mucha's right-hand post. The tie was over as a contest well before half-time and the Goodison crowd, normally so staunch, resorted to abusing their own team, including their erstwhile favourite Marouane Fellaini, who was booed when he was substituted having shown little or no appetite for the fray.

Afterwards Moyes, looking shell-shocked and demoralised, said: "If the fans were disappointed in the players and their body language, if they questioned whether the players were up for the game, then that is their right and they would be right in that criticism.

"People always draw conclusions about my contract situation, or the fact that I have been here for more than a decade, but that game today had nothing to do with those issues. I couldn't say if this was a defining moment."

Martínez will let Dave Whelan, Wigan's 76-year-old owner who broke a leg at Wembley playing for Blackburn Rovers in the 1960 FA Cup final, lead the team out for the semi-final. The Spaniard said: "Going to Wembley is a great thing for the chairman, because he has put this story together and for him it will be an incredible moment, which he deserves.

"But it is also for the fans, for whom following us has been difficult sometimes. It is easy to support success, but they have followed a football club that has been through adversity and defied the odds."